DESIGN OF REACTIVE EQUALIZERS 



735 



However, it is imi)ortaiit to observe that a given value of e automatically 

 determines l)()th the pass-band tolerance and the rate of cut-oflF in the out- 

 band region. Hence, if a specified tolerance is to be realized in the useful 

 band, no control exists over the determination of the resistance elTiciency. 

 Also, it is ap[)arent from Figs. 19 and 20 that small in-band deviations are 

 always obtained at the expense of lower resistance efficiencies, and vice 

 versa. 



Fig. 19— Squared Tchebycheff polynomials, i-Vl{x), for n = 5, and e = 0.5 and « = 0.1. 



Fig. 20— Transfer function expressed in eq. (18) for the values of n and e shown in Fig. 19. 



Returning to the problem of reactive equalization, for // odd, e-F^(.r) 

 may be expressed as 



eWl{x) = e2(Ci.v2 + C.J + • • • + C„.r'"). (19) 



Thus, any A, of eq. (15) is given by aI = e-C . By using the expressions 

 for Fi(.v) through V&{x) tabulated previously, or eq. (17), it is a very simple 

 task to fmd the C, for any desired //. Thus, V\{x) = C\x'- + C2.V'* + • • • -f 

 Cn.v"" is readily ascertained, and the only real problem is the choice of e'-. 

 If /(.V-) has already been chosen, this is accomplished by an addition of 

 /(.V-) and i-Vn{x) for several values of €-. When a c- is found such that 

 the combination, when reciprocated, very closely apjiroximates the specified 

 resistance efficiency, B{x-) is completely defmed. 



